Treatise on Natural Philosophy, Part 1University Press, 1886 - Calculators |
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Page xv
... Root of Determinantal Equation proved negative when Potential Energy is positive for all real Co - ordinates ; positive for some Roots when Potential Energy has negative values ,; but always negative for some Roots - Non - oscillatory ...
... Root of Determinantal Equation proved negative when Potential Energy is positive for all real Co - ordinates ; positive for some Roots when Potential Energy has negative values ,; but always negative for some Roots - Non - oscillatory ...
Page xvi
... Roots with stability - Application of Routh's Theorem - Equal Roots with instability in tran- sitional cases between Stability and Instability - Condi- tions of gyrostatic domination - Gyrostatic Links ex- plained - Gyrostatically ...
... Roots with stability - Application of Routh's Theorem - Equal Roots with instability in tran- sitional cases between Stability and Instability - Condi- tions of gyrostatic domination - Gyrostatic Links ex- plained - Gyrostatically ...
Page 15
... root of the sum of their squares - and the cosines of the inclination of its direction to the given directions are the ratios of the com- ponents to the resultant . It is easy to see that as ds in the limit may be resolved into dr and ...
... root of the sum of their squares - and the cosines of the inclination of its direction to the given directions are the ratios of the com- ponents to the resultant . It is easy to see that as ds in the limit may be resolved into dr and ...
Page 128
... root of a cubic which has two imaginary roots . Again , on the other hand , let the given displacements be made so as to produce a strain of the body with no angular displacement of the principal axes of the strain . Thus three lines of ...
... root of a cubic which has two imaginary roots . Again , on the other hand , let the given displacements be made so as to produce a strain of the body with no angular displacement of the principal axes of the strain . Thus three lines of ...
Page 129
... roots the equation 1 + ( 1 - [ xx ] - [ Yy ] − [ Zz ] ) n + n2 = 0 , whose roots are imaginary if the coefficient of ʼn lies between + 2 and - 2. Now - 2 is evidently its least value , and for that case the roots are real , each being ...
... roots the equation 1 + ( 1 - [ xx ] - [ Yy ] − [ Zz ] ) n + n2 = 0 , whose roots are imaginary if the coefficient of ʼn lies between + 2 and - 2. Now - 2 is evidently its least value , and for that case the roots are real , each being ...
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Common terms and phrases
acceleration action altered angular velocity anticlastic application B₁ Cambridge centre of inertia change of direction circle co-ordinates coefficients component condition configuration constant corresponding curvature curve cycloidal cylinder degrees of freedom Demy 8vo denote diagram differential equation direction cosines distance dt dt dx dy dy dy dy dz ellipse ellipsoid elongation equal equations of motion equilibrium expression finite fixed fluid force function geodetic geometrical given gyrostatic Hence infinitely small initial integral kinetic energy Laplace's equation length moving P₁ parallel parallelepiped particle perpendicular polygon position principal axes quantity radius ratio rectangular right angles rigid body rolling roots rotation round shear simple harmonic simple harmonic motions simple shear solution spherical harmonic spherical surface strain suppose synclastic tangent plane theorem tion twist values whole x₁ y₁ αξ λ² аф